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Harvesting in a Toxic Predator-Prey Model with Carrying Capacity and Maturation Double Delays ZHONG Ying, WEI Yu-ming Chinese Quarterly Journal of Mathematics    2023, 38 (4): 331-348.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.001 Abstract （112）      PDF（pc） （589KB）（76）       Knowledge map    Save  In this paper, a model of predator-prey with dual delay in maturation and carrying capacity is discussed, in which the past activity of the prey should have an impact on the carrying capacity, the mature prey initiates defense mechanisms to release toxins when subjected to predation, and a commercial harvest of the prey is performed. The stability of the equilibrium of the system in the absence of delay is examined and the optimal harvesting strategy of the model is proven. By investigating the roots of the characteristic equation and applying normalized theory, the properties of the coexistence equilibrium of the system and the conditions for the occurrence of the Hopf bifurcation in the neighborhood of the positive equilibrium are described for various combinations of delays. In the end, numerical simulations are used to verify theoretical analysis results. Related Articles | Metrics

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Maximal Resonance of {(3,4),4}-Fullerene Graphs YANG Rui, MA Yan-fei Chinese Quarterly Journal of Mathematics    2024, 39 (1): 1-17.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.001 Abstract （97）      PDF（pc） （551KB）（67）       Knowledge map    Save A {(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4. It follows from Euler’s formula that the number of triangular faces is eight. A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating. Let k be a positive integer, S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern. Moreover, if graph S is k-resonant for any integer k, then S is called maximally resonant. Related Articles | Metrics

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Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions TANG Zhong-hua, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2024, 39 (1): 18-30.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.002 Abstract （97）      PDF（pc） （366KB）（66）       Knowledge map    Save In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed. Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method. Related Articles | Metrics

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Hopf-Rinow Theorem on Convex Complex Finsler Manifolds LI Hong-jun Chinese Quarterly Journal of Mathematics    2024, 39 (1): 31-45.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.003 Abstract （87）      PDF（pc） （365KB）（90）       Knowledge map    Save Suppose (M,F) is a convex complex Finsler manifold. We prove that geodesics of (M,F) are locally minimizing. Hence, F introduces a distance function d such that (M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on (M,F). Related Articles | Metrics

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Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2024, 39 (2): 111-127.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.001 Abstract （84）      PDF（pc） （465KB）（35）       Knowledge map    Save In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0. Related Articles | Metrics

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Minimum Strong Radius of Strong Product Graphs LIU Shu-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (1): 68-72.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.006 Abstract （70）      PDF（pc） （267KB）（37）       Knowledge map    Save A strong product graph is denoted by G1 ⊠G2, where G1 and G2 are called its factor graphs. This paper gives the range of the minimum strong radius of the strong product graph. And using the relationship between the cartesian product graph G1 ×G2 and the strong product graph G1 ⊠G2, another different upper bound of the minimum strong radius of the strong product graph is given. Related Articles | Metrics

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Some New Regularity Criteria for the 3D Boussinesq Equations in Homogeneous Besov Spaces ZOU Mian-lu, LI Qiang Chinese Quarterly Journal of Mathematics    2024, 39 (1): 73-81.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.007 Abstract （69）      PDF（pc） （355KB）（61）       Knowledge map    Save In this paper, we study the regularity criterion for the three-dimensional Boussinesq equations in Besov spaces. We show that the smooth solution (u,θ) is regular if the horizonal velocity uh holds Related Articles | Metrics

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Singularity of Two Kinds of Four Cycle Graphs YOU Xiao-jie, MA Hai-cheng, ZHANG Bin, LI Ya-lan Chinese Quarterly Journal of Mathematics    2023, 38 (4): 349-359.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.002 Abstract （66）      PDF（pc） （361KB）（50）       Knowledge map    Save  Let G be a finite simple graph and A(G) be its adjacency matrix. Then G is singular if A(G) is singular. The graph obtained by bonding the starting vertices and ending vertices of three paths Pa1, Pa2 , Pa3 is called θ-graph, represented by θ(a1,a2,a3). The graph obtained by bonding the two end vertices of the path Ps to the vertices of the θ(a1,a2,a3) and θ(b1,b2,b3) of degree three, respectively, is denoted by α(a1,a2,a3,s,b1,b2,b3) and called α-graph. β-graph is denoted when β(a1,a2,a3,b1,b2,b3) =α(a1,a2,a3,1,b1,b2,b3). In this paper, we give the necessary and sufficient conditions for the singularity of α-graph and β-graph, and prove that the probability that a random given α-graph and β-graph is a singular graph is equal to 1423/2048 and 733/1024 , respectively. Related Articles | Metrics

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Subordination and Superordination Results for a Certain of Integral Operator Involving Generalized Mittag-Leffler Functions WANG Xiao-yuan, LIU Ya-juan Chinese Quarterly Journal of Mathematics    2023, 38 (4): 379-391.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.005 Abstract （59）      PDF（pc） （335KB）（61）       Knowledge map    Save  In the paper, by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function, the authors investigate subclasses of univalent analytic functions, such as starlike functions, convex functions, close-to-convex functions and quasiconvex functions. Several inclusion relationships, inequality properties, subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained. Related Articles | Metrics

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Construction of a Class of Gerstenhaber Algebras HOU Bo, KOU Wen Chinese Quarterly Journal of Mathematics    2023, 38 (4): 370-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.004 Abstract （58）      PDF（pc） （320KB）（68）       Knowledge map    Save For any K-algebra A, based on Hochschild complex and Hochschild cohomology of A, we construct a new Gerstenhaber algebra, and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A. Related Articles | Metrics

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Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br# GUAN Daniel, LIANG Meng-xiang Chinese Quarterly Journal of Mathematics    2024, 39 (2): 200-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.008 Abstract （58）      PDF（pc） （387KB）（30）       Knowledge map    Save  In this paper, we revisit the K¨ahler structures on the affine quadrics M1={z12 +z22 +z32 = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen. Related Articles | Metrics

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Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy LIU Gong-wei, YANG Kun Chinese Quarterly Journal of Mathematics    2024, 39 (1): 97-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.010 Abstract （57）      PDF（pc） （348KB）（32）       Knowledge map    Save We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions. Related Articles | Metrics

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Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity PAN Jia-hui, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2023, 38 (4): 360-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.003 Abstract （56）      PDF（pc） （358KB）（137）       Knowledge map    Save  In this paper, we study the initial boundary value problem of pseudo-parabolic p-Laplacian type equation, which be use to model some important physical and biological phenomena. By using the potential well method, we obtain the global existence, asymptotic behavior and blow up results of weak solution with subcritical initial energy. Then we also extend these results to the critical initial energy. Related Articles | Metrics

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Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm HONG Yong, ZHAO Qian Chinese Quarterly Journal of Mathematics    2024, 39 (1): 59-67.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.005 Abstract （53）      PDF（pc） （330KB）（63）       Knowledge map    Save Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space. Related Articles | Metrics

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Exact Boundary Controllability for a 1-D Second-Order Quasilinear Hyperbolic System WANG Ke, PAN Pan-pan Chinese Quarterly Journal of Mathematics    2023, 38 (4): 424-440.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.010 Abstract （52）      PDF（pc） （365KB）（40）       Knowledge map    Save In this paper, we propose a second-order quasilinear hyperbolic system. By means of the theory on semi-global C1solution to first-order quasilinear hyperbolic systems, we establish the existence and uniqueness of semi-global C2solution to this second-order quasilinear hyperbolic system. After then, the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system. Keywords: First-order quasilinear hyperbolic system; Second-order quasilinear hyperbolic system; Semi-global solution; Exact boundary controllability Related Articles | Metrics

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The Existence and Uniqueness of Self–Dual Monopole Solutions in Gauge Field Theory CHEN Xiao Chinese Quarterly Journal of Mathematics    2024, 39 (1): 86-96.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.009 Abstract （51）      PDF（pc） （316KB）（34）       Knowledge map    Save Magnetic monopoles stand for the static solution arising from a (1+ 3)– dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity. Related Articles | Metrics

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The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix ZENG Min, YUAN Yong-xin Chinese Quarterly Journal of Mathematics    2023, 38 (4): 401-409.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.007 Abstract （49）      PDF（pc） （347KB）（86）       Knowledge map    Save The representation for the Moore-Penrose inverse of the matrix A B C D  is derived by using the solvability theory of linear equations, where A∈Cm×n, B∈Cm×p, C∈Cq×n and D∈Cq×p, with which some special cases are discussed. Related Articles | Metrics

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Sure Independence Screening via Semiparameteric Copula Learning XIN Xin, XIE Bo-yi, LIU Ke-ke Chinese Quarterly Journal of Mathematics    2024, 39 (2): 144-160.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.003 Abstract （46）      PDF（pc） （393KB）（36）       Knowledge map    Save  This paper is concerned with ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula (CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation, conditional mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly improve the performance of feature screening. We establish the sure screening property for the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models. At last, we also illustrate the CC-SIS through a real data example. Related Articles | Metrics

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A Remark on Equivalence between Two Formulas of the Two-point Witten-Kontsevich Correlators GUO Jin-dong Chinese Quarterly Journal of Mathematics    2024, 39 (1): 82-85.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.008 Abstract （45）      PDF（pc） （291KB）（53）       Knowledge map    Save We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by Bertola-Dubrovin-Yang and by Zograf, respec-tively. Related Articles | Metrics

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On the Number of F-Points Inside a Convex F-Polygon GUO Zi-huan, WEI Xiang-lin Chinese Quarterly Journal of Mathematics    2024, 39 (1): 46-58.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.004 Abstract （44）      PDF（pc） （470KB）（15）       Knowledge map    Save An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12, f(12) = 12 Related Articles | Metrics